Distribution of secondary wand boosts

[Manxome]

You know how each student gets +1 in a couple random skills, aside from their main wand skill? I seem to get those secondary boosts in lightning & air about twice as often as in other elements. Anyone else notice something like this?

[Manxome]

Цитата допису ulzgoroth:

I'm terribly curious why the distribution would be as uneven as your data rather strongly suggests.

I've seen an awful lot of RNG bugs in my time. Computer random number generators are non-ideal in subtle ways, reasoning about non-deterministic algorithms is hard, and humans have terrible intuitions about randomness.


Picking which elements to boost is actually slightly tricky from an algorithm perspective, because you're not allowed to pick the same element twice, and you're not allowed to pick the wand's main element, so you can't just generate independent random numbers. There's a few ways you might do it, but here's one way:

1. Put all possible elements in a row.
   
2. Pick the first random element from just the first 6 elements, instead of all 7...
   
3. ...but, if you picked an element equal or to the right of the wand element, shift 1 further right. (For instance, if the wand element is #3, and you picked #5, then shift to #6.)
   
4. Similar strategy for the second random element: choose from just the first 5 elements now, but shift right based on the relative location of both of the previous elements.

Or, in pseudocode:

Represent the 7 possible elements with the numbers from 1 to 7
set W = the wand's element
set X = random number from 1 to 6
if (X >= W) then
    set X = X +1
set Y = random number from 1 to 5
if (Y >= W) then
    set Y = Y + 1
if (Y >= X) then
    set Y = Y + 1
    if (Y == W) then set Y = Y+1

This will correctly give you a uniform distribution over all element combinations, with no collisions. (Unless I've made an embarrassing mistake.)

However, suppose you were a little careless, and instead of writing >=, you wrote ==.

That will still prevent collisions, where you'd pick an element you already had. But now, your first random pick can't land on element #7 unless the wand element was #6, and if the wand element was anything else then you have 2x chance of landing on the element right after it. Similarly, your second random element can't land on #6 unless one of the previous elements was exactly #5, and can't land on #7 unless the previous elements included #5 AND #6.

Consequently, element #6 will be rare, #7 will be even rarer, and both will only appear together with certain other elements.


Now, I'm pretty sure they didn't do exactly that, because if they did, then it shouldn't be possible to get element #7 at all without having element #6 as either the wand element or the other random element. But I've gotten fire without water AND water without fire, so those can't map to elements #6 and #7 in this particular bug.


(The way I'd recommend picking 2 random elements to boost is to create a copy of the full list of elements, remove the wand element, pick a random from what's left, remove the one you picked, and then pick another random. This would be inefficient if the list was big (because you're copying it), but since there's only 7 elements, the cost is too small to risk something more complex (with a higher chance of bugs) unless it's performance-critical code.)

[glitzerpaillette]

You need lots more data if you want to make any significant deductions as to the code.

From a recently started school, I can offer a list that has the advantage of being unculled (which I'm hoping means I didn't send anyone home yet)
Air student: First D N Second L
Air student: First D N Second F
Air student: First N W Second F
Dark student: First E L Second E
Dark student: First A L Second F
Dark student: First A E Second N
Earth student: First A L Second W
Fire student: First E W Second N
Lightning student: First F N Second W
Lightning student: First E N Second D
Lightning student: First A E Second A
Lightning student: First A E Second F
Nature student: First A L Second W
Nature student: First E F Second L
Water student: First A L Second F

While I can see a lot of lightning and air as secondary elements on the first tier when the main wasn't either of them, air and earth runs a close second, considering I have quite a large number of lightning and air students.
I also see fire and water quite often appearing on the second tier.

[Morghean]

Totally random...
I've spent 300 days to get a Gifted Shattered Water mage with +4 Lightning and with FCBS stats...
Now I'm burning my 400th day to get the same kind of mage but with +4 Nature sub spells...
So random that it hurts (mosty my SSD)

...and in the future I'd need a "perfect" tank nukers too... (8E/6L + 2x8A/6F)

[Manxome]

glitzerpaillette, can you confirm that those 15 students you listed are the first 15 you summoned in that save file, with no gaps? Seems surprising you didn't graduate or hire any students before getting tier 2 wands. Also, did you list them in chronological order, or some other order?

I've noticed a couple suspicious patterns.

If I combine your data with mine, we have a total of 5 students who had fire as a random tier 1 boost. Out of those 5, three of them had nature as the other random tier 1 boost, and the other two had nature as the wand skill. None got fire without nature.

Additionally, in our combined data, we summoned a total of 3 students who had fire as their primary (wand) element. Assuming that your data is chronological, then in all 3 cases, the next student summoned after the fire wand had fire as a random tier 1 boost. Not every random fire boost was preceded by a fire wand, but every fire wand was immediately followed by a random fire boost.

Those aren't very large sample sizes, because neither of us has much fire, but it's still a bit surprising.